1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nezavi [6.7K]
2 years ago
7

(7 + 7i)(2 − 2i)

Mathematics
1 answer:
Ostrovityanka [42]2 years ago
3 0

The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)

\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)

\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

=21-21i

After converting into the exponential form:

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

You might be interested in
A laptop computer is purchased for $1850 . After each year, the resale value decreases by 35% . What will the resale value be af
Natali [406]

Answer:

1850 * 0.7^3 = 634.55

Step-by-step explanation:

7 0
3 years ago
The scale of a map says that 4 cm represents 5 km.
vaieri [72.5K]

Answer:

16 cm

Step-by-step explanation:

4 cm represents 5 km. There is a total length of 20 km, so you do 20/5=4. Since you have to multiply 5 by 4 to get 20, you also multiply 4cm by 4, and you get 16, or the amount of cm that represents 20 km.

8 0
3 years ago
What integer is equivalent to 25^3/2
Andreas93 [3]
25^3/2 = (5^2)^3/2 = 5^(2*(3/2)) = 5^3 = 125

hope this will help you 
6 0
3 years ago
Can someone help me for this question please? Why I got wrong answer. ASAP!!!
Snowcat [4.5K]

Answer:

a=8.06

A=29.74

B=60.26

Step-by-step explanation:

This is a right angled triangle and Pythagoras theorem is to be obeyed.

To get c, we follow the Pythagoras rule that says

Hyp² = Opp² + Adj²

c= Hypotenuse

c²= a² + b²

c² = 4² + 7²

c² = 65

c = √65 = 8.06

For angle A,

the opposing side to the angle = a = 4

The adjacent side to the angle = b = 7

Following trigonometry rule.

Tan A = opp/adj

Tan A = 4/7

A = Tan–¹(4/7)

A = 29.74°

For angle B,

Opposing side = 7

Adjacent side = 4

Tan B = 7/4

B = Tan-¹(7/4)

B = 60.26°

5 0
3 years ago
Consider the quadratic equation below. 4x^2-5=3x+4 Determine the correct set-up for solving the equation using the quadratic for
Kipish [7]
4x²-5=3x+4
4x²-3x-9=0

x=(3±√((-3)²-4*4*-9))/2*4

x=3±√(9+144) /8

x=(3±√153) /8

x=⅜±√153/8
4 0
3 years ago
Other questions:
  • Which of the following is a factor of x^3-4x^2-18x+9
    11·2 answers
  • How do you write 649,058,102 in expanded form?
    13·2 answers
  • A train is traveling at a consistent speed.
    11·1 answer
  • PLZ HELP<br><br> The scale factor of ____ was applied to the first triangle.
    9·1 answer
  • How many groups of four shirts can you choose from six shirts? Determine if the word problem is a permutation or a combination,
    9·1 answer
  • Tell whether the angles are adjacent or vertical. Then find the value of x.
    6·2 answers
  • SOMEONE PLEASE TELL ME IN WORDS HOW TO SOLVE THIS
    10·1 answer
  • F – 5.2 1.6 <br><br> answer pls
    10·2 answers
  • 3. Find the length of the missing side using the Pythagorean Theorem. Round to the nearest tenth if necessary.
    8·1 answer
  • Expand each expression A ( x+1)^2 B(x-3)^2. C ( x+4)^2 D (x-1/2)^2
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!